Question

If x^8 +1/x^8
= 47 then x^2 +1/x^2 = ...​

Answer 1

Answer:

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Answer 2

Answer:

The value is $x+\frac1x = \sqrt{5}$

Step-by-step explanation:

• let us consider $x+\frac1x=b$
• Then
  $x^8+\frac1x^8=47\\(x^4+\frac1x^4)^2 = 47+2\\(x^4+\frac1x^4)^2 = 49$
• And if we continue more then we get
  $x^4+\frac1x^4 = 7\\(x^2+\frac1x^2)^2=7+2\\x^2+\frac1x^2 = 3$
• And then
  $x^2+\frac1x^2 = 3\\(x+\frac1x )^2= 3+2\\x+\frac1x = \sqrt{5}$
• So the value is $x+\frac1x = \sqrt{5}$
  #SPJ3